• quasinormal modes
• Hassan Rosen
• black-hole
• perturbation theory
• stability

This thesis deals with the study of black hole solutions in Hassan Rosen's bimetric theory, a nonlinear extension of massive gravity that describes the interaction between two metric fields that is not affected by ghost instability. After the first chapters introducing spherically symmetric spacetimes, quasinormal modes and their application for black holes stability in general relativity, we present Hassan Rosen's theory. We show the existence of solutions that break Lorentz symmetry in the asymptotic region and the relations between the Lorentz breaking parameter and the coupling of the theory. Then Stationary and isotropic solutions are shown to be classified into two Types: (I) and (II), whose structure is analysed. Finally we move to the linearized theory around the backgrounds Provided by (I) and (II). For (I) we show that linear order stability is a consequence of Bianchi identity, which allow us to reduce this case back to general relativity. For solutions (II) we refer to literature that prove the presence of an instability in the monopole sector.